A House panel is calling for slight increases in defense spending over the next decade–which are more than currently projected but not as much as House Republicans previously sought.

The GOP-led House Budget Committee kicked off broad budget discussions with the Senate and White House Tuesday by releasing its version of a non-binding budget resolution, dubbed The Path to Prosperity. The panel, run by former vice presidential candidate Rep. Paul Ryan (R-Wis.), seeks $560.2 billion for defense spending in fiscal year 2014.

While the White House has not yet released a spending plan for that fiscal year, which starts Oct. 1, it sought a smaller $525.4 billion defense budget for FY ’13, the current fiscal year. Also, a continuing resolution the House and Senate are working on for the remainder of FY ’13 likely will give the Pentagon the equivalent of an even-smaller $518 billion budget for FY ‘13.

Ryan told reporters Tuesday the new House budget proposal reflects what the Joint Chiefs of Staff and former Defense Secretary Leon Panetta said they need “to maintain national security for the country.”

The 91-page document advocates resisting pressure to “rapidly decrease” defense spending as combat operations in Iraq and Afghanistan wind down. It argues such pressure “has been driven by budget concerns rather than any assessment of the challenges we face internationally–or of what capabilities we want our military to have.” It paraphrases Chairman of the Joint Chiefs of Staff Army Gen. Martin Dempsey expressing concerns about current security challenges, and his belief that there is no foreseeable “peace dividend.”

The House plan seeks more than $6 trillion “to fund our nation’s defense” over the next decade. It acknowledges this is not as much as House Republicans proposed in the past.

“While this is significantly less than the levels in previous budget resolutions passed by the House, it is approximately $500 billion more than will be available absent changes in the Budget Control Act,” the resolution says, referencing the 2011 law that created “sequestration.”

The resolution does not call for stopping the $500 billion in decade-long sequestration cuts to planned defense spending, which started March 1 and will remain absent a replacement plan from Congress to cut the federal deficit.

However, the plan maintains: “This budget puts us on a better course to ensure our troops and military families don’t pay the price for Washington’s failure to budget responsibly,” referring to Congress’ inability to agree on a sequestration-replacement plan.

The Democrat-run Senate Budget Committee is expected to unveil its dueling budget resolution Wednesday, marking the first time Senate Democrats have released such a spending blueprint in four years. It is expected to be starkly different from Ryan’s plan–with the House version seeking to balance the federal budget in a decade, kill parts of President Barack Obama’s health-care reform, and fundamentally change Medicaid.

House and Senate Democrats quickly slammed  the House resolution, with House Minority Whip Steny Hoyer (D-Md.) criticizing it for keeping the defense sequestration cuts. The White House issued a statement faulting Ryan’s plan for seeking tax breaks for wealthy Americans and a major Medicare overhaul.

“While the House Republican budget aims to reduce the deficit, the math just doesn’t add up,” the White House said.

Obama plans to travel to Capitol Hill Wednesday to meet with House Republicans, and Thursday to see Senate Republicans and House Democrats. He met with Senate Democrats in the Capitol building Tuesday.

As the House and Senate fight over their clashing budget resolutions in the coming weeks, the White House is preparing to release its official FY ’14 budget. Congressional aides have been saying the White House will roll out its spending plan on April 8. Obama spokesman Jay Carney all but confirmed that date Tuesday, telling reporters the massive document will emerge “probably the week of April 8, I would expect.”